Fundamental mathematics
University of Antwerp research units working in the fundamental mathematics areas of algebra, geometry and topology have long been recognised both in Flanders and internationally as centres for excellence in research in fundamental structural mathematics.
This research area concentrates on the fields of noncommutative algebraic geometry and categorical topology. As far as the algebraic-geometric aspect is concerned, this means studying sheaves, localisations, graded and filtered rings, projective spaces, derived algebraic geometry, homological and homotopical algebra, deformation and Hochschild cohomology, deformation quantisation and Hopf algebra. The analytical-topological aspect, on the other hand, is concerned with topological categories, topological spaces, "approach" theory, metrically generated theories, linear algebraic theories, point-free topology and "frames", Clifford analysis and invariant operators.
These theories have their roots in a multitude of often very varied inherently mathematical problems from both directly and indirectly related mathematical fields, including approximation theory, measure and probability theory, and functional and complex analysis. Theories stemming from geometric algebra and Clifford analysis, in particular, also have several applications in theoretical physics.
This research area concentrates on the fields of noncommutative algebraic geometry and categorical topology. As far as the algebraic-geometric aspect is concerned, this means studying sheaves, localisations, graded and filtered rings, projective spaces, derived algebraic geometry, homological and homotopical algebra, deformation and Hochschild cohomology, deformation quantisation and Hopf algebra. The analytical-topological aspect, on the other hand, is concerned with topological categories, topological spaces, "approach" theory, metrically generated theories, linear algebraic theories, point-free topology and "frames", Clifford analysis and invariant operators.
These theories have their roots in a multitude of often very varied inherently mathematical problems from both directly and indirectly related mathematical fields, including approximation theory, measure and probability theory, and functional and complex analysis. Theories stemming from geometric algebra and Clifford analysis, in particular, also have several applications in theoretical physics.
Reputation
The research is being conducted by eight members of the Tenured Academic Personnel and nine post-doctoral researchers. At present, around thirty University of Antwerp researchers are working on this type of research in total. Several of these researchers have received awards and become members of the academy; several are also editors-in-chief of international journals (Applied Categorical Structures, Algebras and Representation Theory, Springer) and monograph series (Mathematical Modelling: Theory and Applications and Algebra and Applications, Springer). In total, the spearhead has produced over 600 articles, published in international journals, as well as around 50 books (20 authored and 30 edited). Fifty PhDs have also been supervised and obtained at the University of Antwerp.
While the University of Antwerp's research on fundamental mathematics clearly receives global recognition, our specific profile and the quality of the research conducted here also means that we occupy a unique place among the Flemish universities.
While the University of Antwerp's research on fundamental mathematics clearly receives global recognition, our specific profile and the quality of the research conducted here also means that we occupy a unique place among the Flemish universities.
Collaboration
Around 30 international workshops and 20 congresses have been organised at the University of Antwerp and over 100 international researchers have come to spend a period of time working with us. We have international contacts and research agreements with various centres around the world, including IHES, Max Planck, UC Berkeley and MIT.
Funding
Researchers working as spokespeople or supervisors in this spearhead have received extensive support from a range of funds, including Science (x2), Human Capital, TMR, RTN, Marie Curie RTN, Intas, GOA (x2) and Research Foundation Flanders (x4). Research Foundation Flanders has also provided around 25 aspirant grants and 15 postdoctoral fellowships.